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Title:A Donsker theorem for Lévy measures PDF Logo
Authors:Nickl, Richard
Reiß, Markus
Issue Date:2012
Series/Report no.:SFB 649 discussion paper 2012-003
Abstract:Given n equidistant realisations of a Lévy process (Lt; t >= 0), a natural estimator for the distribution function N of the Lévy measure is constructed. Under a polynomial decay restriction on the characteristic function, a Donsker-type theorem is proved, that is, a functional central limit theorem for the process in the space of bounded functions away from zero. The limit distribution is a generalised Brownian bridge process with bounded and continuous sample paths whose covariance structure depends on the Fourier-integral operator. The class of Lévy processes covered includes several relevant examples such as compound Poisson, Gamma and self-decomposable processes. Main ideas in the proof include establishing pseudo-locality of the Fourier-integral operator and recent techniques from smoothed empirical processes.
Subjects:uniform central limit theorem
nonlinear inverse problem
smoothed empirical processes
pseudo-differential operators
jump measure
JEL:C14
C22
Document Type:Working Paper
Appears in Collections:SFB 649 Discussion Papers, HU Berlin

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